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AI- modelling of molecular identification and feminization of wolbachia infected Aedes aegypti
Progress in Biophysics and Molecular Biology xxx (xxxx) xxx
Contents lists available at ScienceDirect
Progress in Biophysics and Molecular Biology journal homepage: www.elsevier.com/locate/pbiomolbio
AI- modelling of molecular identification and feminization of wolbachia infected Aedes aegypti Mehwish Iftikhar a, Sahrish Iftikhar b, Ayesha Sohail a, Sana Javed a, c, * a
Department of Mathematics, Comsats University Islamabad, Lahore Campus, 54000, Pakistan Department of Zoology, GC University, Lahore, Pakistan c Department of Biochemistry and Biophysics, Stockholm University, Science for Life Laboratory, Box 1031, 17121, Solna, Sweden b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 22 May 2019 Received in revised form 23 June 2019 Accepted 6 July 2019 Available online xxx
Background: The genetic control strategies of vector borne diseases includes the replacement of a vector population by “disease-refractory” mosquitoes and the release of mosquitoes with a gene to control the vector's reproduction rates. Wolbachia are common intracellular bacteria that are found in arthropods and nematodes. Wolbachia infected male mosquitos have been used in different experimental trials around the world to suppress the target population of Aedes aegypti and this genetic control strategy has proved to be a promising alternative to other treatment strategies. Due to certain limitations, the successful application of this strategy is still awaited. Methods: Mathematical frame work for Wolbachia induced genetic control strategy has been developed in this article. With the aid of Artificial Intelligence (AI) tools, accurate parametric values are depicted. For the first time, the model is well synchronized with the experimental findings. The model is comprised of the generalized varying coefficient and multiple mating rates between infected and uninfected compartments of Aedes aegypti dengue to forecast the disease control. Results: Two mathematical models are developed in this article to demonstrate different mating rates of the genetic control strategy. The important parameters and time varying coefficients are well demonstrated with the aid of numerical computations. The resulting thresholds and forecasting may prove to be a useful tool for future experimental studies. Conclusions: From our analysis, we have concluded that the genetic control strategy is a promising technique and the role of Wolbachia infected male mosquitos, in genetic control strategies, can be better interpreted in an inexpensive manner with the aid of a theoretical model. © 2019 Published by Elsevier Ltd.
Keywords: Dengue reproduction inhibition Genetic control Dynamical analysis Kinetic modelling Numerical simulations
1. Introduction Vector-borne diseases, primarily those spread by mosquitoes contribute extensively in human morbidity and mortility. Dengue is in fact a major source of contamination, hospitalization, and death in subtropical areas Burattini et al. (2008). Before 1970, merely 9 countries reported rigorous dengue plague. The virus is now prevalent in more than 100 countries in the WHO regions of Africa, the Americas, the Eastern Mediterranean, South-East Asia and the Western Pacific Dejnirattisai et al. (2016). Dengue fever, chikungunya, and Zika virus are in the list of
* Corresponding author. Department of Mathematics, Comsats Institute of Information Technology, Lahore 54000, Pakistan. E-mail addresses: [email protected] (A. Sohail), sana.javed@scilifelab. se (S. Javed).
world's most threatening arthropod-borne viral diseases Gibbons and Vaughn (2002); Roth et al. (2014). Ae. Aegypti is a parasite and is found in humid areas. Ae. Aegypti can strain in unhygienic water or small collection of water such as flower vases or coconut shells etc. Malavige et al. (2004). Aedes albopictus, recognized as the “Asian tiger mosquito”, serves as a secondary vector. This species feeds on humans at places such as in gardens, parks and bushes around human residences, and in the day light, especially in the morning, it is reported in Japan and other Asian countries Higa (2011). No accurate treatment exists for this deadly disease. Very recently, the world's first dengue vaccine has been approved for use, yet its effectiveness is inadequate and diverse for different virus serotypes, population, age groups, and countries Capeding et al. (2014); Villar et al. (2015). There exist conventional control policies in countries, where dengue cases are frequently reported,
https://doi.org/10.1016/j.pbiomolbio.2019.07.001 0079-6107/© 2019 Published by Elsevier Ltd.
Please cite this article as: Iftikhar, M et al., AI- modelling of molecular identification and feminization of wolbachia infected Aedes aegypti, Progress in Biophysics and Molecular Biology, https://doi.org/10.1016/j.pbiomolbio.2019.07.001
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M. Iftikhar et al. / Progress in Biophysics and Molecular Biology xxx (xxxx) xxx
such policies are focusing on techniques to control the population of Aedes mosquito vectors, but such attempts unfortunately remained unsuccessful in reducing the existing burden of the pandemic. The number of dengue cases has increased 30 folds over the past 50 years Lam et al. (2011). Each year, roughly 400 million people are infected by dengue virus in more than 100 countries Kyle and Harris (2008) around the world, while the other one-third of the world's population is under its threat. Dengue virus (DENV) is a serious challenge in tropical areas, and is affecting the health budgets with over half of the world's population at risk. Unlike other epidemiological diseases, the dengue virus is not only transmitted horizontally, but it also transmits vertically and is thus more efficient in its rapid transmission. Dengue virus is transmitted between humans by the infectious bite of the mosquito Ae. Aegypti and, to some extent by Ae. Albopictus. In the absence of a tetravalent vaccine and antiviral drugs or therapies, approaches to suppress dengue outbreaks typically focus on controlling the mosquito vector. Current vector control methods rely mostly on insecticide use to reduce larval and/or adult populations of Ae. Aegypti, particularly during dengue outbreaks. Although insecticides are useful for controlling mosquito populations at small geographic scales and when vector populations are high, they also have non-target effects on other insects, may accumulate and pollute the environment, and over time lead to the evolution of insecticide resistance. Moreover, they are often prohibitively expensive for use as a preventative measure in public health programs in many developing countries. These issues have motivated the researchers to provide some alternative control measures, including biological control methods that reduce or eliminate the reliance on insecticidal toxins. Over the past century, different studies focusing on this issue have been reported. Recently, it has been demonstrated by the research group led by Hurst et al. (2012) that “wMelPop infection inhibits the ability of a range of pathogens to infect Aedes aegypti.” There are many strategies to use Wolbachia for disease suppression programmes particularly for viral disease spread by mosquito vectors. Wolbachia is a group of maternally inherited endosymbionts which are widely distributed in invertebrate species including various insects. It is well known for causing a number of reproductive modifications (cytoplasmic incompatibility, parthenogenesis, male killing) in its host. Wolbachia has an important characteristic feature to inhibit transmission of various parasites or pathogens through its host vector. The release of Wolbachia infected females can spread Wolbachia strain in natural population however, can also produce, positive or negative fitness effects under seasonally variable environment. Wolbachia induces resistance to dengue virus in Ae. Aegypti and limits transmission of dengue virus in Ae. Albopictus. Increasing attention has been paid to control the spread of these diseases by targeting mosquito longevity by introducing genetically modified mosquitoes or introducing endosymbiotic Wolbachia bacteria to shorten the mosquito lifespan (see Walker et al. (2011); Lam et al. (2011); Villar et al. (2015) and the references therein for details). The Wolbachia-infected mosquitoes are released to create a sustained infection in the wild (Wolbachia-free) population. If the infection is sustained, then the wild infected mosquitoes will be less effective in transmitting these diseases. Inspired from the recent experimental findings of Iftikhar Iftikhar (2017), where a semi-field evaluation of the competitiveness of Wolbachia infected Ae. Aegypti males for the suppression of dengue vector population was reported, we have derived for the very first time, four different mathematical models demonstrating the horizontal as well as the vertical transmissions of the Wolbachia infected Ae. Aegypti and the resulting disease control thresholds. Our mathematical model will not only help in understanding the underlying dynamics that are needed to create a
sustained endemic Wolbachia infection, but will also provide a benchmark in understanding the interaction rates of infected and uninfected Ae. Aegypti males with the females, which will surely help in anticipating the mating rates and thus the thresholds.
2. Mathematical models We have developed four models by considering four cases, describing population dynamics of aquatic stage (A) that includes the eggs, larvae, and pupae stages, adult male (M), and adult female (F) mosquitoes. The population dynamics of dengue mosquitoes without introducing Wolbachia have been investigated in case 1 and is thus called a negative control group. The interactions between the male infected and female uninfected group, the male uninfected and the female uninfected group, are coupled together in a model discussed in case 2 and is termed as an Hr group. In case 3 the interactions between the male infected and female uninfected group are discussed and is termed as the Hi group. In case 4 the compartmental modelling is executed only between the infected aquatic, male and female mosquitos and is thus termed as the Hw group.
2.1. Negative control case study In this case, the mosquitoes are grouped into three compartments: Wolbachia-free aquatic stage AN , Wolbachia-free female mosquitoes FN and Wolbachia-free male mosquitoes MN as shown in schematic diagram (Fig. 1). The death rates of uninfected male and female mosquitoes are kept the same, i.e. equal to mN in a manner similar to Ruang Ruang-areerate and Kittayapong (2006). Death rate of uninfected aquatic stage of mosquitoes is mNA . Development rate of uninfected aquatic stage is gN . The carrying capacity of aquatic stage of mosquitoes is represented by K. The parametric values are considered according to the standard transmission rates of compartmental models Brauer (2008), i.e. careful sensitivity analysis was conducted with the aid of commercially available software MATCONT theoretically, and with the aid of detailed analysis of experimental studies Capeding et al. (2014); Walker et al. (2011). The rate of change of the density of uninfected mosquitos and their aquatic stages over a specific period of time can thus be demonstrated by a nonlinear system of ordinary differential equations as follows:
Fig. 1. Compartmental model of the dengue mosquito reproduction and mating (Eq. (1)).
Please cite this article as: Iftikhar, M et al., AI- modelling of molecular identification and feminization of wolbachia infected Aedes aegypti, Progress in Biophysics and Molecular Biology, https://doi.org/10.1016/j.pbiomolbio.2019.07.001
M. Iftikhar et al. / Progress in Biophysics and Molecular Biology xxx (xxxx) xxx
8 > > > d rN AN > > A FN MN mNA AN gN AN 1 ¼ > N > > dt FN þ MN K > > > > > > < d FN ¼ ð1 εN ÞgN AN mN FN > dt > > > > > > > > > >d > M ¼ εN gN AN mN MN > > : dt N
3
uninfected male with uninfected female were kept equal to rN and rWN . Besides the birth and death rates, as described in the mathe-
(1)
For the sake of simplicity, the system can further be reduced to two differential equations by assuming ε ¼ 0:5. In the numerical simulations, as presented in section 3, we have kept this constant equal to ε ¼ 0:45, for better interpretation and to keep distinction between male and female groups.
2.2. Hr group case study In this case four compartments are considered: Wolbachia-free aquatic stage AN , Wolbachia-free female mosquitoes FN , Wolbachia-free male mosquitoes MN , and Wolbachia infected male mosquitoes MW . In this case additional mating group of uninfected females and infected males is introduced. By introducing such group theoretically, we have actually introduced the cytoplasmic incompatibility (a processes that leads to the death of embryos before hatching). This incompatibility is infact a reproductive advantage, since the incompatibility between the sperm and eggs (of Wolbachia-infected males and non-Wolbachia females) induced by Wolbachia infection has made Wolbachia treatment a competent candidate among other dengue control studies Hurst et al. (2012). The mating rates for Wolbachia infected male and
Table 1 Ratios between uninfected male and Wolbachia infected male.
matical model 1, a very critical time dependent coefficient “wðtÞ” is considered in our mathematical model to demonstrate this incompatibility and its consequences on total number of aquatic stages. From the schematic diagram (Fig. 3), it is evident that the cytoplasmic incompatibility inhibits the aquatic stage whereas the uninfected mosquito mating enhances it. Another important feature of this study is that, the dengue control is synchronized in the model through the Hill function formulation. Hill function is used in drug therapy models where the function is derived using the kinetic modelling that explains the drug-disease interaction Likhoshvai and Ratushny (2007). We have considered a normalized function, which is dependent on the infected male and uninfected female mating through a parameter g, i.e. g increases relative to higher number of infected male mosquitos in the compartment. In this article, inspired from the experimental work of Iftikhar (2017), we have considered four different frequencies of the infected male mosquitos (as shown in Table 1). The ratio between infected and uninfected males was varied to observe the impact on the mating and on the resulting suppression of the dengue. The variable x is taken as a linear function of the independent variable t, and is normalized to avoid computational complexity.
wðKxÞ ¼
Kxg a þ Kxg
(2)
This non-dimensional entity wðtÞ when incorporated in equation (1) of model 3, provided a useful tool to trace the cytoplasmic incompatibility. This impact is demonstrated with the aid of graphical interpretation in Fig. 2. The details of the analysis are provided in section 3.
2.3. Hi group
Groups
Male Ratio
MN :MW
FN
g
Hr1 Hr2 Hr3 Hr4
1:1 1:2 1:3 1:4
15:15 15:30 15:45 15:60
20 20 20 20
1 2 3 4
The male infected and female uninfected groups were considered in the laboratory for this study. A simple mathematical model for this study was simulated, since only cytoplasmic incompatibility was observed and thus an exponential decay in the population size of mosquitos in the compartments was observed.
Fig. 2. AN density, with and without cytoplasmic incompatibility.
Please cite this article as: Iftikhar, M et al., AI- modelling of molecular identification and feminization of wolbachia infected Aedes aegypti, Progress in Biophysics and Molecular Biology, https://doi.org/10.1016/j.pbiomolbio.2019.07.001
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Fig. 3. Compartmental model of the dengue mosquito reproduction and mating in Hr group (Eq. (3)).
8 > > > d AN FN ðrN MN þ rWN MW Þ > > > A 1 ¼ w mN AN gN AN gN AN N > CI > dt FN þ MN þ MW K > > > > >d > > > < FN ¼ ð1 εN ÞgN AN mN FN dt > >d > > MN ¼ εN gN AN mN MN > > > dt > > > > >d > > MW ¼ mW AW > > : dt
2.4. Positive control group The negative control group discussed in case 1 provides a useful tool to forecast the dengue outbreak in the absence of any treatment strategy. A similar model, where the study is conducted on the “infected-only” male female and aquatic mosquitos, will lead to a positive control strategy where the Wolbachia infected mosquitos maintain transmission among themselves. We have not considered this case for numerical simulations since it will eventually lead to dynamics which will only be possible where there are zero uninfected mosquitos. Such analysis is far from reality and is thus not entertained.
(3)
application on the data provided in Table 1. For this purpose, we have used MATCONT Dhooge et al. (2008) for the sensitivity analysis of the models and only suitable parametric values were used for the numerical simulations. Furthermore, the equlibria can also be obtained using the matlab smart tools. We have used the optimality tool box of Matlab for this purpose. The first order optimality graph for case 1 ia presented in Fig. 4. Next, we have simulated the results for the negative control group. The results presented in
3. Numerical analysis 3.1. Data analysis For the numerical analysis of the computational model and for the parametric evaluation, we first used the AI advanced support vector machine learning algorithm for classification of male and female mosquito, prior and posterior to the treatment. We analyzed the data obtained over different seasons for the field weather data of “temperature” and “relative humidity”. The details of the statistical analysis are provided in the supplementary material (S1). 3.2. Graphical analysis The cases discussed in section 2 describes special cases to test the dengue control under special treatment of Wolbachia mating. The validity of the mathematical models is mandatory before their
Fig. 4. First order optimality conditions for equilibria of case 1.
Please cite this article as: Iftikhar, M et al., AI- modelling of molecular identification and feminization of wolbachia infected Aedes aegypti, Progress in Biophysics and Molecular Biology, https://doi.org/10.1016/j.pbiomolbio.2019.07.001
M. Iftikhar et al. / Progress in Biophysics and Molecular Biology xxx (xxxx) xxx
Fig. 5 demonstrates two types of dynamics relative to two different values of rN . The number of aquatic mosquitos reached approximately 4000 after 10 days when the mating rates were higher, on the other hand, for lower mating rates (depending on other
5
environmental conditions), this number was only around 2000 after 40 days. In Figs. 6e8 the dynamics for the Hr group are presented relative to different initial conditions as described in Table 1. The dynamical
Fig. 5. Hc (negative control) group's dynamics over longer time period relative to mating rate.
Please cite this article as: Iftikhar, M et al., AI- modelling of molecular identification and feminization of wolbachia infected Aedes aegypti, Progress in Biophysics and Molecular Biology, https://doi.org/10.1016/j.pbiomolbio.2019.07.001
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Fig. 6. Hr1 group dynamical analysis relative to aquatic stage.
Fig. 7. Hr2 group dynamical analysis relative to aquatic stage.
analysis is well presented with the aid of phase space portraits in the top panel of these images. We can see that as the initial value for the infected male mosquitos increased, the amplitude of the threshold value for AN decreased. Thus there was an inverse
relation between control and initial number of Wolbachia males. This fact is well demonstrated in Fig. 9. Thus the mathematical modelling of the Hr group was in close agreement with the experimental findings presented in S1, where different initial
Please cite this article as: Iftikhar, M et al., AI- modelling of molecular identification and feminization of wolbachia infected Aedes aegypti, Progress in Biophysics and Molecular Biology, https://doi.org/10.1016/j.pbiomolbio.2019.07.001
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Fig. 8. Hr3 group dynamical analysis relative to aquatic stage.
physically motivated by experimental work Iftikhar (2017) and unlike other available models in literature, our models are solely based on realistic transmissions. One of our future goals is to couple this model with a mosquito-human model to demonstrate the spread of dengue. Such study can further be extended to explore other vector borne diseases such as Chikungunya, and Zika virus. Conflicts of interest The authors declare that there is no conflict of interest. Acknowledgments: The authors would like to acknowledge the support provided by the department of Zoology, Government College University (GCU), Lahore, Pakistan for the successful conduction of experimental work. The supplementary material provided has been extracted from the research thesis of Ms Sahrish Iftikhar. Fig. 9. Variation in AN density in Hr1, Hr2 and Hr3 groups relative to time.
Appendix A. Supplementary data conditions resulted in different dynamics subject to a class of variable control measures. From the numerical simulations, we conclude that the dengue suppression via Wolbachia infected males can be well demonstrated with the aid of compartmental models. 4. Conclusions and future work In this article, the dengue mosquito genetic transmission and its control measures are well demonstrated with the aid of kinetic modelling, schematic description and the resulting state of the art model, that fully establishes the treatment-disease interactions. The models presented in this article are novel since these are
Supplementary data to this article can be found online at https://doi.org/10.1016/j.pbiomolbio.2019.07.001. References Brauer, F., 2008. Compartmental models in epidemiology. In: Mathematical Epidemiology. Springer, pp. 19e79. Burattini, M., Chen, M., Chow, A., Coutinho, F., Goh, K., Lopez, L., Ma, S., Massad, E., 2008. Modelling the control strategies against dengue in Singapore. Epidemiol. Infect. 136 (3), 309e319. Capeding, M.R., Tran, N.H., Hadinegoro, S.R.S., Ismail, H.I.H.M., Chotpitayasunondh, T., Chua, M.N., Luong, C.Q., Rusmil, K., Wirawan, D.N., Nallusamy, R., et al., 2014. Clinical efficacy and safety of a novel tetravalent dengue vaccine in healthy children in asia: a phase 3, randomised, observermasked, placebo-controlled trial. The Lancet 384 (9951), 1358e1365. Dejnirattisai, W., Supasa, P., Wongwiwat, W., Rouvinski, A., Barba-Spaeth, G.,
Please cite this article as: Iftikhar, M et al., AI- modelling of molecular identification and feminization of wolbachia infected Aedes aegypti, Progress in Biophysics and Molecular Biology, https://doi.org/10.1016/j.pbiomolbio.2019.07.001
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Duangchinda, T., Sakuntabhai, A., Cao-Lormeau, V.-M., Malasit, P., Rey, F.A., et al., 2016. Dengue virus sero-cross-reactivity drives antibody-dependent enhancement of infection with zika virus. Nat. Immunol. 17 (9), 1102. Dhooge, A., Govaerts, W., Kuznetsov, Y.A., Meijer, H.G.E., Sautois, B., 2008. New features of the software matcont for bifurcation analysis of dynamical systems. Math. Comput. Model. Dyn. Syst. 14 (2), 147e175. Gibbons, R.V., Vaughn, D.W., 2002. Dengue: an escalating problem. BMJ 324 (7353), 1563e1566. Higa, Y., 2011. Dengue vectors and their spatial distribution. Trop. Med. Health 39, 4SUPPLEMENT):S17eS27. Hurst, T.P., Pittman, G., O’neill, S.L., Ryan, P.A., Le Nguyen, H., Kay, B.H., 2012. Impacts of wolbachia infection on predator prey relationships: evaluating survival and horizontal transfer between w melpop infected aedes aegypti and its predators. J. Med. Entomol. 49 (3), 624e630. Iftikhar, S., 2017. Semi-field Evaluation of the Competitiveness of Wolbachia Infected Aedes aegypti Males for the Suppression of Dengue Vector Population. PhD thesis. GC University Lahore. Kyle, J.L., Harris, E., 2008. Global spread and persistence of dengue. Annu. Rev. Microbiol. 62, 71e92. Lam, S.K., Burke, D., Capeding, M.R., Chong, C.K., Coudeville, L., Farrar, J., Gubler, D., Hadinegoro, S.R., Hanna, J., Lang, J., et al., 2011. Preparing for introduction of a
dengue vaccine: recommendations from the 1st dengue v2v asia-pacific meeting. Vaccine 29 (51), 9417e9422. Likhoshvai, V., Ratushny, A., 2007. Generalized hill function method for modeling molecular processes. J. Bioinform. Comput. Biol. 5 (02b), 521e531. Malavige, G., Fernando, S., Fernando, D., Seneviratne, S., 2004. Dengue viral infections. Postgrad. Med. J. 80 (948), 588e601. Roth, A., Mercier, A., Lepers, C., Hoy, D., Duituturaga, S., Benyon, E., Guillaumot, L., Souares, Y., 2014. Concurrent outbreaks of dengue, chikungunya and zika virus infectionsean unprecedented epidemic wave of mosquito-borne viruses in the pacific 2012e2014. Euro Surveill. 19 (41), 20929. Ruang-areerate, T., Kittayapong, P., 2006. Wolbachia transinfection in aedes aegypti: a potential gene driver of dengue vectors. Proc. Natl. Acad. Sci. 103 (33), 12534e12539. Villar, L., Dayan, G.H., Arredondo-García, J.L., Rivera, D.M., Cunha, R., Deseda, C., Reynales, H., Costa, M.S., Morales-Ramírez, J.O., Carrasquilla, G., et al., 2015. Efficacy of a tetravalent dengue vaccine in children in Latin america. N. Engl. J. Med. 372 (2), 113e123. Walker, T., Johnson, P., Moreira, L., Iturbe-Ormaetxe, I., Frentiu, F., McMeniman, C., Leong, Y., Dong, Y., Axford, J., Kriesner, P., et al., 2011. The wmel wolbachia strain blocks dengue and invades caged aedes aegypti populations. Nature 476 (7361), 450.
Please cite this article as: Iftikhar, M et al., AI- modelling of molecular identification and feminization of wolbachia infected Aedes aegypti, Progress in Biophysics and Molecular Biology, https://doi.org/10.1016/j.pbiomolbio.2019.07.001
Contents lists available at ScienceDirect
Progress in Biophysics and Molecular Biology journal homepage: www.elsevier.com/locate/pbiomolbio
AI- modelling of molecular identification and feminization of wolbachia infected Aedes aegypti Mehwish Iftikhar a, Sahrish Iftikhar b, Ayesha Sohail a, Sana Javed a, c, * a
Department of Mathematics, Comsats University Islamabad, Lahore Campus, 54000, Pakistan Department of Zoology, GC University, Lahore, Pakistan c Department of Biochemistry and Biophysics, Stockholm University, Science for Life Laboratory, Box 1031, 17121, Solna, Sweden b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 22 May 2019 Received in revised form 23 June 2019 Accepted 6 July 2019 Available online xxx
Background: The genetic control strategies of vector borne diseases includes the replacement of a vector population by “disease-refractory” mosquitoes and the release of mosquitoes with a gene to control the vector's reproduction rates. Wolbachia are common intracellular bacteria that are found in arthropods and nematodes. Wolbachia infected male mosquitos have been used in different experimental trials around the world to suppress the target population of Aedes aegypti and this genetic control strategy has proved to be a promising alternative to other treatment strategies. Due to certain limitations, the successful application of this strategy is still awaited. Methods: Mathematical frame work for Wolbachia induced genetic control strategy has been developed in this article. With the aid of Artificial Intelligence (AI) tools, accurate parametric values are depicted. For the first time, the model is well synchronized with the experimental findings. The model is comprised of the generalized varying coefficient and multiple mating rates between infected and uninfected compartments of Aedes aegypti dengue to forecast the disease control. Results: Two mathematical models are developed in this article to demonstrate different mating rates of the genetic control strategy. The important parameters and time varying coefficients are well demonstrated with the aid of numerical computations. The resulting thresholds and forecasting may prove to be a useful tool for future experimental studies. Conclusions: From our analysis, we have concluded that the genetic control strategy is a promising technique and the role of Wolbachia infected male mosquitos, in genetic control strategies, can be better interpreted in an inexpensive manner with the aid of a theoretical model. © 2019 Published by Elsevier Ltd.
Keywords: Dengue reproduction inhibition Genetic control Dynamical analysis Kinetic modelling Numerical simulations
1. Introduction Vector-borne diseases, primarily those spread by mosquitoes contribute extensively in human morbidity and mortility. Dengue is in fact a major source of contamination, hospitalization, and death in subtropical areas Burattini et al. (2008). Before 1970, merely 9 countries reported rigorous dengue plague. The virus is now prevalent in more than 100 countries in the WHO regions of Africa, the Americas, the Eastern Mediterranean, South-East Asia and the Western Pacific Dejnirattisai et al. (2016). Dengue fever, chikungunya, and Zika virus are in the list of
* Corresponding author. Department of Mathematics, Comsats Institute of Information Technology, Lahore 54000, Pakistan. E-mail addresses: [email protected] (A. Sohail), sana.javed@scilifelab. se (S. Javed).
world's most threatening arthropod-borne viral diseases Gibbons and Vaughn (2002); Roth et al. (2014). Ae. Aegypti is a parasite and is found in humid areas. Ae. Aegypti can strain in unhygienic water or small collection of water such as flower vases or coconut shells etc. Malavige et al. (2004). Aedes albopictus, recognized as the “Asian tiger mosquito”, serves as a secondary vector. This species feeds on humans at places such as in gardens, parks and bushes around human residences, and in the day light, especially in the morning, it is reported in Japan and other Asian countries Higa (2011). No accurate treatment exists for this deadly disease. Very recently, the world's first dengue vaccine has been approved for use, yet its effectiveness is inadequate and diverse for different virus serotypes, population, age groups, and countries Capeding et al. (2014); Villar et al. (2015). There exist conventional control policies in countries, where dengue cases are frequently reported,
https://doi.org/10.1016/j.pbiomolbio.2019.07.001 0079-6107/© 2019 Published by Elsevier Ltd.
Please cite this article as: Iftikhar, M et al., AI- modelling of molecular identification and feminization of wolbachia infected Aedes aegypti, Progress in Biophysics and Molecular Biology, https://doi.org/10.1016/j.pbiomolbio.2019.07.001
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such policies are focusing on techniques to control the population of Aedes mosquito vectors, but such attempts unfortunately remained unsuccessful in reducing the existing burden of the pandemic. The number of dengue cases has increased 30 folds over the past 50 years Lam et al. (2011). Each year, roughly 400 million people are infected by dengue virus in more than 100 countries Kyle and Harris (2008) around the world, while the other one-third of the world's population is under its threat. Dengue virus (DENV) is a serious challenge in tropical areas, and is affecting the health budgets with over half of the world's population at risk. Unlike other epidemiological diseases, the dengue virus is not only transmitted horizontally, but it also transmits vertically and is thus more efficient in its rapid transmission. Dengue virus is transmitted between humans by the infectious bite of the mosquito Ae. Aegypti and, to some extent by Ae. Albopictus. In the absence of a tetravalent vaccine and antiviral drugs or therapies, approaches to suppress dengue outbreaks typically focus on controlling the mosquito vector. Current vector control methods rely mostly on insecticide use to reduce larval and/or adult populations of Ae. Aegypti, particularly during dengue outbreaks. Although insecticides are useful for controlling mosquito populations at small geographic scales and when vector populations are high, they also have non-target effects on other insects, may accumulate and pollute the environment, and over time lead to the evolution of insecticide resistance. Moreover, they are often prohibitively expensive for use as a preventative measure in public health programs in many developing countries. These issues have motivated the researchers to provide some alternative control measures, including biological control methods that reduce or eliminate the reliance on insecticidal toxins. Over the past century, different studies focusing on this issue have been reported. Recently, it has been demonstrated by the research group led by Hurst et al. (2012) that “wMelPop infection inhibits the ability of a range of pathogens to infect Aedes aegypti.” There are many strategies to use Wolbachia for disease suppression programmes particularly for viral disease spread by mosquito vectors. Wolbachia is a group of maternally inherited endosymbionts which are widely distributed in invertebrate species including various insects. It is well known for causing a number of reproductive modifications (cytoplasmic incompatibility, parthenogenesis, male killing) in its host. Wolbachia has an important characteristic feature to inhibit transmission of various parasites or pathogens through its host vector. The release of Wolbachia infected females can spread Wolbachia strain in natural population however, can also produce, positive or negative fitness effects under seasonally variable environment. Wolbachia induces resistance to dengue virus in Ae. Aegypti and limits transmission of dengue virus in Ae. Albopictus. Increasing attention has been paid to control the spread of these diseases by targeting mosquito longevity by introducing genetically modified mosquitoes or introducing endosymbiotic Wolbachia bacteria to shorten the mosquito lifespan (see Walker et al. (2011); Lam et al. (2011); Villar et al. (2015) and the references therein for details). The Wolbachia-infected mosquitoes are released to create a sustained infection in the wild (Wolbachia-free) population. If the infection is sustained, then the wild infected mosquitoes will be less effective in transmitting these diseases. Inspired from the recent experimental findings of Iftikhar Iftikhar (2017), where a semi-field evaluation of the competitiveness of Wolbachia infected Ae. Aegypti males for the suppression of dengue vector population was reported, we have derived for the very first time, four different mathematical models demonstrating the horizontal as well as the vertical transmissions of the Wolbachia infected Ae. Aegypti and the resulting disease control thresholds. Our mathematical model will not only help in understanding the underlying dynamics that are needed to create a
sustained endemic Wolbachia infection, but will also provide a benchmark in understanding the interaction rates of infected and uninfected Ae. Aegypti males with the females, which will surely help in anticipating the mating rates and thus the thresholds.
2. Mathematical models We have developed four models by considering four cases, describing population dynamics of aquatic stage (A) that includes the eggs, larvae, and pupae stages, adult male (M), and adult female (F) mosquitoes. The population dynamics of dengue mosquitoes without introducing Wolbachia have been investigated in case 1 and is thus called a negative control group. The interactions between the male infected and female uninfected group, the male uninfected and the female uninfected group, are coupled together in a model discussed in case 2 and is termed as an Hr group. In case 3 the interactions between the male infected and female uninfected group are discussed and is termed as the Hi group. In case 4 the compartmental modelling is executed only between the infected aquatic, male and female mosquitos and is thus termed as the Hw group.
2.1. Negative control case study In this case, the mosquitoes are grouped into three compartments: Wolbachia-free aquatic stage AN , Wolbachia-free female mosquitoes FN and Wolbachia-free male mosquitoes MN as shown in schematic diagram (Fig. 1). The death rates of uninfected male and female mosquitoes are kept the same, i.e. equal to mN in a manner similar to Ruang Ruang-areerate and Kittayapong (2006). Death rate of uninfected aquatic stage of mosquitoes is mNA . Development rate of uninfected aquatic stage is gN . The carrying capacity of aquatic stage of mosquitoes is represented by K. The parametric values are considered according to the standard transmission rates of compartmental models Brauer (2008), i.e. careful sensitivity analysis was conducted with the aid of commercially available software MATCONT theoretically, and with the aid of detailed analysis of experimental studies Capeding et al. (2014); Walker et al. (2011). The rate of change of the density of uninfected mosquitos and their aquatic stages over a specific period of time can thus be demonstrated by a nonlinear system of ordinary differential equations as follows:
Fig. 1. Compartmental model of the dengue mosquito reproduction and mating (Eq. (1)).
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8 > > > d rN AN > > A FN MN mNA AN gN AN 1 ¼ > N > > dt FN þ MN K > > > > > > < d FN ¼ ð1 εN ÞgN AN mN FN > dt > > > > > > > > > >d > M ¼ εN gN AN mN MN > > : dt N
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uninfected male with uninfected female were kept equal to rN and rWN . Besides the birth and death rates, as described in the mathe-
(1)
For the sake of simplicity, the system can further be reduced to two differential equations by assuming ε ¼ 0:5. In the numerical simulations, as presented in section 3, we have kept this constant equal to ε ¼ 0:45, for better interpretation and to keep distinction between male and female groups.
2.2. Hr group case study In this case four compartments are considered: Wolbachia-free aquatic stage AN , Wolbachia-free female mosquitoes FN , Wolbachia-free male mosquitoes MN , and Wolbachia infected male mosquitoes MW . In this case additional mating group of uninfected females and infected males is introduced. By introducing such group theoretically, we have actually introduced the cytoplasmic incompatibility (a processes that leads to the death of embryos before hatching). This incompatibility is infact a reproductive advantage, since the incompatibility between the sperm and eggs (of Wolbachia-infected males and non-Wolbachia females) induced by Wolbachia infection has made Wolbachia treatment a competent candidate among other dengue control studies Hurst et al. (2012). The mating rates for Wolbachia infected male and
Table 1 Ratios between uninfected male and Wolbachia infected male.
matical model 1, a very critical time dependent coefficient “wðtÞ” is considered in our mathematical model to demonstrate this incompatibility and its consequences on total number of aquatic stages. From the schematic diagram (Fig. 3), it is evident that the cytoplasmic incompatibility inhibits the aquatic stage whereas the uninfected mosquito mating enhances it. Another important feature of this study is that, the dengue control is synchronized in the model through the Hill function formulation. Hill function is used in drug therapy models where the function is derived using the kinetic modelling that explains the drug-disease interaction Likhoshvai and Ratushny (2007). We have considered a normalized function, which is dependent on the infected male and uninfected female mating through a parameter g, i.e. g increases relative to higher number of infected male mosquitos in the compartment. In this article, inspired from the experimental work of Iftikhar (2017), we have considered four different frequencies of the infected male mosquitos (as shown in Table 1). The ratio between infected and uninfected males was varied to observe the impact on the mating and on the resulting suppression of the dengue. The variable x is taken as a linear function of the independent variable t, and is normalized to avoid computational complexity.
wðKxÞ ¼
Kxg a þ Kxg
(2)
This non-dimensional entity wðtÞ when incorporated in equation (1) of model 3, provided a useful tool to trace the cytoplasmic incompatibility. This impact is demonstrated with the aid of graphical interpretation in Fig. 2. The details of the analysis are provided in section 3.
2.3. Hi group
Groups
Male Ratio
MN :MW
FN
g
Hr1 Hr2 Hr3 Hr4
1:1 1:2 1:3 1:4
15:15 15:30 15:45 15:60
20 20 20 20
1 2 3 4
The male infected and female uninfected groups were considered in the laboratory for this study. A simple mathematical model for this study was simulated, since only cytoplasmic incompatibility was observed and thus an exponential decay in the population size of mosquitos in the compartments was observed.
Fig. 2. AN density, with and without cytoplasmic incompatibility.
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Fig. 3. Compartmental model of the dengue mosquito reproduction and mating in Hr group (Eq. (3)).
8 > > > d AN FN ðrN MN þ rWN MW Þ > > > A 1 ¼ w mN AN gN AN gN AN N > CI > dt FN þ MN þ MW K > > > > >d > > > < FN ¼ ð1 εN ÞgN AN mN FN dt > >d > > MN ¼ εN gN AN mN MN > > > dt > > > > >d > > MW ¼ mW AW > > : dt
2.4. Positive control group The negative control group discussed in case 1 provides a useful tool to forecast the dengue outbreak in the absence of any treatment strategy. A similar model, where the study is conducted on the “infected-only” male female and aquatic mosquitos, will lead to a positive control strategy where the Wolbachia infected mosquitos maintain transmission among themselves. We have not considered this case for numerical simulations since it will eventually lead to dynamics which will only be possible where there are zero uninfected mosquitos. Such analysis is far from reality and is thus not entertained.
(3)
application on the data provided in Table 1. For this purpose, we have used MATCONT Dhooge et al. (2008) for the sensitivity analysis of the models and only suitable parametric values were used for the numerical simulations. Furthermore, the equlibria can also be obtained using the matlab smart tools. We have used the optimality tool box of Matlab for this purpose. The first order optimality graph for case 1 ia presented in Fig. 4. Next, we have simulated the results for the negative control group. The results presented in
3. Numerical analysis 3.1. Data analysis For the numerical analysis of the computational model and for the parametric evaluation, we first used the AI advanced support vector machine learning algorithm for classification of male and female mosquito, prior and posterior to the treatment. We analyzed the data obtained over different seasons for the field weather data of “temperature” and “relative humidity”. The details of the statistical analysis are provided in the supplementary material (S1). 3.2. Graphical analysis The cases discussed in section 2 describes special cases to test the dengue control under special treatment of Wolbachia mating. The validity of the mathematical models is mandatory before their
Fig. 4. First order optimality conditions for equilibria of case 1.
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Fig. 5 demonstrates two types of dynamics relative to two different values of rN . The number of aquatic mosquitos reached approximately 4000 after 10 days when the mating rates were higher, on the other hand, for lower mating rates (depending on other
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environmental conditions), this number was only around 2000 after 40 days. In Figs. 6e8 the dynamics for the Hr group are presented relative to different initial conditions as described in Table 1. The dynamical
Fig. 5. Hc (negative control) group's dynamics over longer time period relative to mating rate.
Please cite this article as: Iftikhar, M et al., AI- modelling of molecular identification and feminization of wolbachia infected Aedes aegypti, Progress in Biophysics and Molecular Biology, https://doi.org/10.1016/j.pbiomolbio.2019.07.001
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Fig. 6. Hr1 group dynamical analysis relative to aquatic stage.
Fig. 7. Hr2 group dynamical analysis relative to aquatic stage.
analysis is well presented with the aid of phase space portraits in the top panel of these images. We can see that as the initial value for the infected male mosquitos increased, the amplitude of the threshold value for AN decreased. Thus there was an inverse
relation between control and initial number of Wolbachia males. This fact is well demonstrated in Fig. 9. Thus the mathematical modelling of the Hr group was in close agreement with the experimental findings presented in S1, where different initial
Please cite this article as: Iftikhar, M et al., AI- modelling of molecular identification and feminization of wolbachia infected Aedes aegypti, Progress in Biophysics and Molecular Biology, https://doi.org/10.1016/j.pbiomolbio.2019.07.001
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Fig. 8. Hr3 group dynamical analysis relative to aquatic stage.
physically motivated by experimental work Iftikhar (2017) and unlike other available models in literature, our models are solely based on realistic transmissions. One of our future goals is to couple this model with a mosquito-human model to demonstrate the spread of dengue. Such study can further be extended to explore other vector borne diseases such as Chikungunya, and Zika virus. Conflicts of interest The authors declare that there is no conflict of interest. Acknowledgments: The authors would like to acknowledge the support provided by the department of Zoology, Government College University (GCU), Lahore, Pakistan for the successful conduction of experimental work. The supplementary material provided has been extracted from the research thesis of Ms Sahrish Iftikhar. Fig. 9. Variation in AN density in Hr1, Hr2 and Hr3 groups relative to time.
Appendix A. Supplementary data conditions resulted in different dynamics subject to a class of variable control measures. From the numerical simulations, we conclude that the dengue suppression via Wolbachia infected males can be well demonstrated with the aid of compartmental models. 4. Conclusions and future work In this article, the dengue mosquito genetic transmission and its control measures are well demonstrated with the aid of kinetic modelling, schematic description and the resulting state of the art model, that fully establishes the treatment-disease interactions. The models presented in this article are novel since these are
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Please cite this article as: Iftikhar, M et al., AI- modelling of molecular identification and feminization of wolbachia infected Aedes aegypti, Progress in Biophysics and Molecular Biology, https://doi.org/10.1016/j.pbiomolbio.2019.07.001